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Register a new userThe point-charge self-energy in Lee-Wick Theories
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Added by
Fabricio Augusto Barone Rangel PhD
Publication date
2015
fields
Physics
and research's language is
English
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In this paper we study the ultraviolet and infrared behaviour of the self energy of a point-like charge in the vector and scalar Lee-Wick electrodynamics in a $d+1$ dimensional space time. It is shown that in the vector case, the self energy is strictly ultraviolet finite up to $d=3$ spatial dimensions, finite in the renormalized sense for any $d$ odd, infrared divergent for $d=2$ and ultraviolet divergent for $d>2$ even. On the other hand, in the scalar case, the self energy is striclty finite for $dleq 3$, and finite, in the renormalized sense, for any $d$ odd.
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The Lee-Wick electrodynamics in the vicinity of a conducting plate is investigated. The propagator for the gauge field is calculated and the interaction between the plate and a point-like electric charge is computed. The boundary condition imposed on the vector field is taken to be the one that vanishes, on the plate, the normal component of the dual field strength to the plate. It is shown that the image method is not valid in Lee-Wick electrodynamics.
We propose a type of non-anticommutative superspace, with the interesting property of relating to Lee-Wick type of higher derivatives theories, which are known for their interesting properties, and have lead to proposals of phenomenologicaly viable higher derivatives extensions of the Standard Model. The deformation of superspace we consider does not preserve supersymmetry or associativity in general; however, we show that a non-anticommutative version of the Wess-Zumino model can be properly defined. In fact, the definition of chiral and antichiral superfields turns out to be simpler in our case than in the well known ${cal N}=1/2$ supersymmetric case. We show that, when the theory is truncated at the first nontrivial order in the deformation parameter, supersymmetry is restored, and we end up with a well known Lee-Wick type of higher derivative extension of the Wess-Zumino model. Thus we show how non-anticommutative could provide an alternative mechanism for generation of these kind of higher derivative theories.
Most discussions of propagators in Lee-Wick theories focus on the presence of two massive complex conjugate poles in the propagator. We show that there is in fact only one pole near the physical region, or in another representation three pole-like structures with compensating extra poles. The latter modified Lehmann representation is useful caculationally and conceptually only if one includes the resonance structure in the spectral integral.
We construct a modification of the standard model which stabilizes the Higgs mass against quadratically divergent radiative corrections, using ideas originally discussed by Lee and Wick in the context of a finite theory of quantum electrodynamics. The Lagrangian includes new higher derivative operators. We show that the higher derivative terms can be eliminated by introducing a set of auxiliary fields; this allows for convenient computation and makes the physical interpretation more transparent. Although the theory is unitary, it does not satisfy the usual analyticity conditions.
We propose a new axiom system for unitary quantum field theories on curved space-time backgrounds, by postulating that the partition function and the correlators extend analytically to a certain domain of complex-valued metrics. Ordinary Riemannian metrics are contained in the allowable domain, while Lorentzian metrics lie on its boundary.
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